
Adversarial Robust Low Rank Matrix Estimation: Compressed Sensing and Matrix Completion
We consider robust low rank matrix estimation when random noise is heavy...
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Exact Reconstruction of Euclidean Distance Geometry Problem Using Lowrank Matrix Completion
The Euclidean distance geometry problem arises in a wide variety of appl...
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Completing LowRank Matrices with Corrupted Samples from Few Coefficients in General Basis
Subspace recovery from corrupted and missing data is crucial for various...
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A Characterization of Deterministic Sampling Patterns for LowRank Matrix Completion
Lowrank matrix completion (LRMC) problems arise in a wide variety of ap...
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Binary component decomposition Part II: The asymmetric case
This paper studies the problem of decomposing a lowrank matrix into a f...
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Coherence and sufficient sampling densities for reconstruction in compressed sensing
We give a new, very general, formulation of the compressed sensing probl...
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Numerical comparisons between Bayesian and frequentist lowrank matrix completion: estimation accuracy and uncertainty quantification
In this paper we perform a numerious numerical studies for the problem o...
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Lowrank Matrix Completion in a General Nonorthogonal Basis
This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the lowrank matrix completion problem with sampling under entry sensing or with respect to a symmetric orthonormal basis. The analysis is based on dual certificates using a dual basis approach and does not assume the restricted isometry property (RIP). We introduce a condition on the basis called the correlation condition. This condition can be computed in time O(n^3) and holds for many cases of deterministic basis where RIP might not hold or is NP hard to verify. If the correlation condition holds and the underlying low rank matrix obeys the coherence condition with parameter ν, under additional mild assumptions, our main result shows that the true matrix can be recovered with very high probability from O(nrν^2n) uniformly random expansion coefficients.
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